Your numbers do indeed mirror it pretty well.
You have a bit more of a low-end tail but that could simply be statistical variation. Or it could be due to the raid arena you’re in or many other factors (including that it may not be a binomial distribution but instead a weighted distribution towards the lower tail).
Attack stat increases do indeed affect Damage Over Time special skills. This means that Levelling, Emblems & Troops all increase / change the quantity of DoT dealt via a special skill.
It’s why when a hero is not maxed, it won’t have the full DoT amount, despite having 8/8 special skill already. Also explains the phenomenon you’re describing.
You can read more about it in this comprehensive guide: Understanding DoT (Damage over Time)